I want to explore moderating effects of m1. I also have another moderator m2, and here are the two cases:

(1) reg y c.x##c.m1
(2) reg y c.x##(c.m1 c.m2)

Let's say, the coefficient of the interaction term c.x#c.m1 in Case (1) is significant, but it's insignificant in Case (2).
My question is --- does m1 moderates the effect of x on y?


I kinda guess the answer is No --- because we should follow the regression result in Case (2).
But this get me think, how far should we go? Should we control all the control variables in the interaction before we conclude moderating effect? Should we use the following:

(3) reg y c.x##(c.m1 c.m2 c.control1 c.control2 ...)

But we rarely do (3) in the published paper, the convention is do (1) and (2) in the same regression table. So my question is that why don't we do (3) ?